Abstract
The mathematical description of phase separation and melting processes is often based on phase field models. These descriptions define a phase field variable that specifies particular phases as the solution of a semilinear parabolic partial differential equation. A small parameter that defines the width of the interfaces between different phases enters classical stability estimates in a critical way, and refined arguments are required to improve this dependence. Applying those estimates to analyzing approximation schemes for the simplest case of the Allen–Cahn equation in terms of a priori and a posteriori error estimates is carried out. The stability of various implicit and semi-implicit time-stepping schemes is discussed.
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Bartels, S. (2015). The Allen–Cahn Equation. In: Numerical Methods for Nonlinear Partial Differential Equations. Springer Series in Computational Mathematics, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-13797-1_6
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DOI: https://doi.org/10.1007/978-3-319-13797-1_6
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